Theorem simp3i 1142

Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)

Hypothesis

Ref	Expression
3simp1i.1	⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)

Assertion

Ref	Expression
simp3i	⊢ 𝜒

Proof of Theorem simp3i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)
2		simp3 1139	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
3	1, 2	ax-mp 5	1 ⊢ 𝜒

Syntax hints:   ∧ w3a 1087

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1089

This theorem is referenced by:  hartogslem2  9460  harwdom  9508  divalglem6  16337  structfn  17095  strleun  17096  oppchomfval  17649  sratset  21147  srads  21149  tngip  24603  dfrelog  26542  log2ub  26927  birthdaylem3  26931  birthday  26932  divsqrtsum2  26961  harmonicbnd2  26983  lgslem4  27279  lgscllem  27283  lgsdir2lem2  27305  lgsdir2lem3  27306  mulog2sumlem1  27513  siilem2  30940  h2hva  31062  h2hsm  31063  h2hnm  31064  elunop2  32101  wallispilem3  46425  wallispilem4  46426  prstchomval  49918  cnelsubclem  49962